I put the onus on adventure writing and not the system. I mean, I'm not saying the system has nothing to do with exploration, but I don't think 5E needs changes here. Dungeon crawling is often boring because there is little point beyond kill things and take their stuff. What is the history of the place? What secrets does it hold? Make it interesting to explore and not just a pit to sink resources into again again.
So, probably more stuff in the DMG for GMs to build their own interesting dungeons. Perhaps even a DMG II that focuses on campaign building with a dedicated section on dungeon crawling. Also, adventures that are good, which often WotC ones are not (IMO of course).